Equality of Dedekind sums mod ℤ,2ℤ and 4ℤ

2014/08/15 by Emmanuel Tsukerman · 1 citation
Mathematics · #math.NT

paper · pdf · doi:10.1142/s1793042115500748

3 pages

arxiv created 2014/08/15 · arxiv updated 2014/11/27

Abstract

In [Girstmair, A criterion for the equality of Dedekind sums mod ℤ, Internat. J. Number Theory 10: (2014) 565--568], it was shown that the necessary condition b | (a₁ a₂-1)(a₁-a₂) for equality of two dedekind sums s(a₁,b) and s(a₂,b) given in [Jabuka, Robins and Wang, When are two Dedekind sums equal? Internat. J. Number Theory 7: (2011) 2197--2202] is equivalent to 12s(a₁,b)-12s(a₂,b) ∈ ℤ. In this note, we give a new proof of this result and then find two additional necessary and sufficient conditions for 12s(a₁,b)-12s(a₂,b) ∈ 2ℤ, 4ℤ. These give new necessary conditions on equality of Dedekind sums.

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